Liquid dispensers, such as liquid soap and sanitizer dispensers, provide a user with a predetermined amount of liquid upon the actuation of the dispenser. It is known to dispense liquids, such as soaps, sanitizers, cleansers and disinfectants from a dispenser housing that uses a removable and replaceable cartridge containing the liquid. In addition, it is sometimes desirable to dispense the liquids in the form of foam by, for example, interjecting air into the liquid creating a foamy mixture of liquid and air bubbles. It is also known to dispense liquids from a dispenser housing that uses a removable and replaceable cartridge containing liquid and a foam pump that includes a single pump that pumps air and liquid, both of which are disposed with the replaceable cartridge. Refill units that include a single pump that pumps liquid and air are more costly to manufacture than refill units containing just a liquid pump, require more plastic to make, and cost more to dispose of after the refill unit is empty.